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The Quarterly Journal of Mathematics, 1993
The author considers the differential operator \(H\) acting on \(L^2(- \alpha, +\alpha)\) given by \[ Hf= -{d\over dx} \Biggl(a(x) {df\over dx}\Biggr) \] and subject to Dirichlet boundary conditions at \(-\alpha\) and \(+\alpha\), where \(a: (- \alpha, +\alpha)\to (0, +\infty)\) is measurable with \(\gamma^{- 1}\leq a(x)\leq \gamma\) for all \(x\in (- \
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The author considers the differential operator \(H\) acting on \(L^2(- \alpha, +\alpha)\) given by \[ Hf= -{d\over dx} \Biggl(a(x) {df\over dx}\Biggr) \] and subject to Dirichlet boundary conditions at \(-\alpha\) and \(+\alpha\), where \(a: (- \alpha, +\alpha)\to (0, +\infty)\) is measurable with \(\gamma^{- 1}\leq a(x)\leq \gamma\) for all \(x\in (- \
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Canadian Mathematical Bulletin, 1999
AbstractWe obtain an explicit formula for heat kernels of Lorentz cones, a family of classical symmetric cones. By this formula, the heat kernel of a Lorentz cone is expressed by a function of timetand two eigenvalues of an element in the cone. We obtain also upper and lower bounds for the heat kernels of Lorentz cones.
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AbstractWe obtain an explicit formula for heat kernels of Lorentz cones, a family of classical symmetric cones. By this formula, the heat kernel of a Lorentz cone is expressed by a function of timetand two eigenvalues of an element in the cone. We obtain also upper and lower bounds for the heat kernels of Lorentz cones.
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1996
The goal of the heat kernel method is to express (2.40) as an integral over the fixed point set M γ in M of the transformation γ. Here M γ = M if γ is the identity. The method is based on the following observations about arbitrary elliptic differential operators D, acting on sections of a smooth vector bundle F over a compact manifold M, which admits a
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The goal of the heat kernel method is to express (2.40) as an integral over the fixed point set M γ in M of the transformation γ. Here M γ = M if γ is the identity. The method is based on the following observations about arbitrary elliptic differential operators D, acting on sections of a smooth vector bundle F over a compact manifold M, which admits a
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Neumann Heat Kernel Monotonicity
2014This chapter contains the probabilistic proof of the claim that the Neumann heat kernel in a ball, evaluated on the diagonal, is a monotone function of the distance from the center.
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Heat kernels and theta functions
1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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